Certificate for #2611 ⟨a, b | ababba=bbaa⟩

Completion settings:

• Auxiliary generators:
  1. c = bbaa
• Reduction order:
  • Left-to-right shortlex with a < b < c

Axiom: ababba=bbaa.

Referenced by [3].

Axiom: bbaa=c.

Defines rule #2.

Referenced by [3], [5], [6], [10].

Simplify [1] ababba=bbaa.

Reduce RHS:

Defines rule #4.

Referenced by [4], [5], [6], [7], [9].

Overlap of [3] ababba=c with [3] ababba=c:

Critical pair: ababbc=cbabba.

Flip LHS and RHS.

Referenced by [6], [12].

Overlap of [3] ababba=c with [2] bbaa=c:

Critical pair: abac=ca.

Defines rule #1.

Referenced by [7], [8], [13].

Overlap of [2] bbaa=c with [3] ababba=c:

Critical pair: bbac=cbabba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [9], [10], [11], [12], [14].

Overlap of [3] ababba=c with [5] abac=ca:

Critical pair: ababbca=cbac.

Reduce LHS:

Defines rule #3.

Referenced by [8], [11].

Overlap of [7] bbaca=cbac with [5] abac=ca:

Critical pair: bbacca=cbacbac.

Flip LHS and RHS.

Defines rule #9.

Overlap of [3] ababba=c with [6] ababbc=bbac:

Critical pair: ababbbbac=cbabbc.

Defines rule #10.

Overlap of [2] bbaa=c with [6] ababbc=bbac:

Critical pair: bbabbac=cbabbc.

Defines rule #7.

Overlap of [7] bbaca=cbac with [6] ababbc=bbac:

Critical pair: bbacbbac=cbacbabbc.

Flip LHS and RHS.

Defines rule #12.

Simplify [4] cbabba=ababbc.

Reduce RHS:

Defines rule #6.

Referenced by [13], [14].

Overlap of [12] cbabba=bbac with [5] abac=ca:

Critical pair: cbabbca=bbacbac.

Defines rule #8.

Overlap of [12] cbabba=bbac with [6] ababbc=bbac:

Critical pair: cbabbbbac=bbacbabbc.

Defines rule #11.